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We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) andanti-BRST symmetry invariance of the Lagrangian density of a four (3 +1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can becaptured within the framework of the superfield approach to BRST formalism. Theabove 4D theory, where there is an explicit coupling between the non-Abelian1-form gauge field and the Dirac fields, is considered on a (4, 2)-dimensionalsupermanifold, parameterized by the bosonic 4D space-time variables and a pairof Grassmannian variables. We show that the Grassmannian independence of thesuper Lagrangian density, expressed in terms of the (4, 2)-dimensionalsuperfields, is a clear signature of the presence of the (anti-)BRST invariancein the original 4D theory.

Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: superfield formalism